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Packing parameters in graphs: new bounds and a solution to an open problem


In this paper, we investigate the packing parameters in graphs. By applying the Mantel’s theorem, we give upper bounds on packing and open packing numbers of triangle-free graphs along with characterizing the graphs for which the equalities hold and exhibit sharp Nordhaus–Gaddum type inequalities for packing numbers. We also solve the open problem of characterizing all connected graphs with \(\rho _{o}(G)=n-\omega (G)\) posed in Hamid and Saravanakumar (Discuss Math Graph Theory 35:5–16, 2015).

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We would like to thank the anonymous referee for his/her comments.

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Correspondence to Babak Samadi.

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Mojdeh, D.A., Samadi, B. Packing parameters in graphs: new bounds and a solution to an open problem. J Comb Optim 38, 739–747 (2019).

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  • Packing number
  • Open packing number
  • Nordhaus–Gaddum inequality
  • Open problem
  • Triangle-free graph

Mathematics Subject Classification

  • 05C69